In Japan, it's not so much for intelligibility (though it is in some cases, since some dialects approach "different language" levels) as it is just a cultural thing. In formal contexts, it is simply proper to speak standard/Tokyo Japanese (even in other regions). Not doing so can make you seem disrespectful, or that you're not taking the situation seriously.
For a modern, international comparison, take how many American politicians speak with a southern accent. That would simply not fly in Japan, as it would give the impression that they don't take their job seriously, whereas in the US and many other places, it is simply a regional dialect (although stereotypes may of course apply).
Fun fact: In older times, the formal version of the Kansai dialect was frequently used by prostitutes and geisha, as it sounded "high class" and "sexy". Incidentally, prostitutes weren't viewed as "whores" in any derogatory sense; they were viewed as women of culture and beauty, whereas the "common woman" was simply there to make kids and take care of the home. :p